Abstract
We explore some of the interplay between Brill-Noether subvarieties of the moduli space S U C ( 2 , K ) {\mathcal {SU}}_C(2,K) of rank 2 bundles with canonical determinant on a smooth projective curve and 2 θ 2\theta -divisors, via the inclusion of the moduli space into | 2 Θ | |2\Theta | , singular along the Kummer variety. In particular we show that the moduli space contains all the trisecants of the Kummer and deduce that there are quadrisecant lines only if the curve is hyperelliptic; we show that for generic curves of genus > 6 >6 , though no higher, bundles with > 2 >2 sections are cut out by Γ 00 \Gamma _{00} ; and that for genus 4 this locus is precisely the Donagi-Izadi nodal cubic threefold associated to the curve.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
